"muzzle energy" versus ft./lbs. of energy

[Ned Kelly]

For many years I have wondered why an unusual calculation is always used to determine a bullets power when it contradicts the true determination of Ft/lbs of energy.

Muzzle energy = weight in grains x (velocity in feet per second squared) / 450240 or 450380 depending on your source.

Ft. lbs. = weight in lbs x velocity

In the case of bullets this is determined by weight in grains/ 7040( which is the number of grains in one lb.) x velocity.

i.e.

.223 with 55 grain bullet at 3300 ft per sec = 25.8 ft lbs of energy VS 1330 ft. lbs of energy

.308 with 150 grain at 2800 = 59.6 VS 2611

.45 acp 230 grain at 850 = 27.8 VS 369

12 guage slug with 440 grain at 1600 = 100 VS 2502

Interestingly enough Taylors KO formula also takes into consideration bullet momentum in the calculation. Its only modifier is that he included the bullet diameter. He also simpified the figure 7040 into 7000 even.

Bullet momentum is directly related to how much effect the bullet will have on a steel plate or in the actual force delivered to an animal or man.

So why do the gun magazines and ballistics table use "muzzle energy"?

Are you still a skeptic?

Than take into consideration the felt recoild between a .308 and a 12 guage slug round. The 12 guage easily has almost twice the recoil. When we compare actual bullet momentum between the two........

59.6 VS 100 we can easily see the ratio is very close to what we feel in recoil. Keep also in consideration that for every action there is an equal and opposite reaction.

If the 12 guage and .308 share similiar "muzzle energy" than why would the 12 guage kick harder?

 

[CypherNinja]

weight in lbs x velocity

That is not energy, it's momentum.

 

[akodo]

as a bullet passes through the air, it looses speed.

this means it has a different ft/lb rating at 0, 50, 100, 200, 500 etc distance.

muzzle energy simply means ft/lb rating at distance zero

also, your equation for energy is wrong. Velocity is squared

 

[ants]

You need a little additional work on the matter.

ft.-lb. (sometimes noted lb-ft) is a unit of measure of energy. Muzzle energy is a gun tech term for energy at the muzzle.

Momentum isn't the same thing. The force on an object is what makes the momentum change. Net force on an object equals the rate at which its momentum changes.

In physics, a force is a push or pull that can cause an object with mass to change its velocity. Force has both magnitude and direction, making it a vector quantity. Newton's second law states that an object with a constant mass will accelerate in proportion to the net force acting upon and in inverse proportion to its mass.

It is generally accepted that there are 7000 grains in one pound, although certain conversion formulae arrive at 6999.990 grains.

 

[JSmith]

And I'd always thought that what I really wanted to know was kinetic energy at impact:

Ek=1/2(m*v-squared)

(m in kg, v in meters/sec, and Ek in joules...)

 

[benEzra]

There are 7000 grains in a pound avoirdupois (aka U.S. pound, pound mass), not 7040.

(Yes, for the engineers out there, the U.S. pound is a unit of mass, defined as exactly 0.45359237 of the mass of the SI kilogram/IPK.)

Muzzle energy is merely kinetic energy of the bullet as it exits the muzzle, and may be measured in ft/lb, joules/kilojoules, or whatever unit of energy you wish to use.

A 55-grain bullet at 3300 ft/sec (3.564 grams at 1005.84 meters per second) has a kinetic energy at the muzzle of:

1802.84421 J
1.80284421 kJ
1,329.71 ft-lb
4.30581 x 10^-10 kilotons of TNT

Its momentum in SI units is 3.585 kg-m/s, and its relativistic Lorentz transformation gamma is 1.00000000000562842.

 

[Ned Kelly]

I found the answer I needed. Thanks for you help.

http://www.bautforum.com/archive/index.php/t-39231.html

as a bullet passes through the air, it looses speed.

this means it has a different ft/lb rating at 0, 50, 100, 200, 500 etc distance.

muzzle energy simply means ft/lb rating at distance zero

also, your equation for energy is wrong. Velocity is squared

No, I have it right when discussing ft lbs/ sec.

When discussing firearms energy i did factor in sqauring velocity.

Some engineers do not consider using the pound when measuring force to be acceptable.

When determining momentum it is acceptable.

So I think I will be abandoning the firearms industry energy measurments in favor of the true ft. lbs./sec formula. Which is also used in determining gun recoil.

m*v= ft. lbs./sec is definitely superior in my opinion. It puts into perspective what is really going on when a bullet hits its target.

There are 7000 grains in a pound avoirdupois (aka U.S. pound, pound mass), not 7040.

I stand corrected. Taylor uses 7000 in his KO factor calculation as well.

 

[benEzra]

The "firearms industry energy measurements" are the same as any other way to calculate energy:

E = 1/2 * m * v^2

regardless of what units you use.

Mass * velocity is not any variety of energy. It is momentum, which is a completely different measurement.

Energy and momentum tell you different things. A 55-grain .223 at 3000 ft/sec and a baseball thrown at 60 ft/sec have comparable momentum, but quite different effects when they hit something, due to the different kinetic energy.

 

[Ned Kelly]

Mass * velocity is not any variety of energy. It is momentum, which is a completely different measurement.

But to me it is more relevant when figuring out the effects of bullet impact on a target.


force is not really telling me anything about what that projectile will really do, but momentum will.

I think telling people a cartridge delivers 1300 ft. lbs. of force has more eye candy appeal than telling them it only has 26 ft. lbs. of momentum.

 

[benEzra]

Kinetic energy is not force; it is energy. A gunwriter who says in a magazine that a cartridge produces 1300 ft-lb of "force" (and yes, I have seen that) is no less clueless than if he had said his electric bill was for 1850 kW-h of "force". Energy is energy, not force.

Some ways to express energy (and momentum too) do involve force and distance units, but they are not measures of either. 1330 ft-lb is merely a different and perhaps confusing way of saying 1800 watt-seconds, 1.8 kJ, or however many calories, ergs, or BTU that works out to.

Both energy and momentum are important in understanding bullet effects, but momentum is more important for low velocity projectiles, and energy is more important at higher velocities.

 

[JohnBT]

"So I think I will be abandoning the firearms industry energy measurments in favor of the true ft. lbs./sec formula. Which is also used in determining gun recoil."

Recoil is a slightly different calculation than figuring what the projectile is doing. Recoil calculations need to include the total weight of all the ejecta - bullet or shot, powder, wad, etc. depending on what you are shooting.

John

 

[mljdeckard]

Yes, and FELT recoil is different again from recoil, as many things in the configuration of the weapon, from spring weight to bore axis can affect felt recoil.

 

[Suicide*Ride]

benEzra said - momentum is more important for low velocity projectiles, and energy is more important at higher velocities.

Why?

 

[jakemccoy]

Ft-lbs is the American measurement of energy.

I prefer metric (Joules). So be it. Do a conversion. Better yet, don't.

 

[meef]

"The sum of the square root of two sides of an isosceles triangle is equal to the square root of the third side." - the Scarecrow upon receiving his brain from the Wizard

The Scarecrow, however, also got it wrong you'll note.

 

[Ned Kelly]

So Kinetic energy is simply a method to determine how much energy is in an object. In metric it is measured in Joules. In America we use standard and do not have a comparable word so we use ft. lbs.

Momentum or impetus however is much easier to understand. And its value would be crucial to any projectile. However it is also measure in ft. lbs.

So it is pretty obvious that there is a lot of confusion over the name of both. Maybe we should all switch to metric.

However as I have said before Momentum is the more important when considering bullet impact.

So I am learning a bit as I go. I have always used kinetic energy in my ballistics since the 80s but I always felt that something was definitely missing between what the numbers (kinetic energy) says and what happens downrange when a steel plate is hit.

 

[kyo]

its physics, there is another thread on this already.

 

[RyanM]

Momentum or impetus however is much easier to understand. And its value would be crucial to any projectile. However it is also measure in ft. lbs.

No, it's not. Energy is measured in force times distance. 1 ft-lb = 1 pound of force applied over a distance of 1 foot.

So 1 ft-lb = 1 ft * 1 lb

So for instance, a bullet with 400 ft-lbs of energy fired from a gun with a 6 inch barrel, had an average of 800 pounds of force applied to it over 1/2 foot distance. 800 lb * 1/2 ft = 400 ft-lbs. It's actually more complicated than that and involves calculus, but the average force must be 800 lbs, to get 400 ft-lbs of energy at the muzzle of a 6" barrel.

There is no "per second" anywhere in the basic definition of the foot-pound, even though it can be expressed in terms of slugs of mass and feet per second. For instance, if you applied 800 pounds of force over 6" distance to a car, the car would get 400 ft-lbs of energy. But obviously, it would take a much longer time to push a 3,000 pound car than a 1/2 ounce bullet, with the same pounds of force. If we assume the car weighs 3217.4 pounds, to make the math easier, it would be moving at about 2.83 fps, by the time you've pushed for 6 inches (with 800 pounds of force).

Momentum is measured in mass times velocity. 1 sg-ft/sec = 1 slug (unit of mass, equal to about 32.174 pounds) times 1 foot/second.

1 sg-ft/sec = 1 sg * 1 ft/sec

 

[ants]

I get the impression Mr. Kelly is less interested in math and physics. He's more interested in getting a handle on the concept of momentum so he can use it to his best benefit in comparing bullets. Nothing wrong with that.

Of course, I suppose you can use any measure that suits your interest as long as you're consistent.

In the Real World, terminal ballistics (the effect of the bullet upon the target) involves the construction of the bullet, the nature of the target, and plenty of factors not included in the mathematical formulae.

For an interesting basic primer, go to the Hornady web site and find their treatise on internal ballistics, external ballistics, and terminal ballistics.

 

[JohnKSa]

Muzzle energy = weight in grains x (velocity in feet per second squared) / 450240 or 450380 depending on your source.

That is not muzzle energy.

Sticking with standard (vs. metric) here are the formulas.

Muzzle energy (or kinetic energy) = weight x velocity x velocity /450437

Where muzzle energy is in ft-lbs (ft x lbs), weight is in grains and velocity is in feet per second.

The basic formula is:

kinetic energy = 1/2 x mass x velocity x velocity

The large number in the denominator of the more commonly seen version listed above is the result of multiplying the conversion factor that takes grains to mass by the 2 in the 1/2 of the formula.

Momentum or impetus however is much easier to understand. And its value would be crucial to any projectile. However it is also measure in ft. lbs.

Your units are not correct.

Momentum is mass x velocity, with the units being being lb-s (lbs x seconds). (RyanM is also correct, but he's expressed his momentum formula and units in terms of slugs rather than lbs)

force is not really telling me anything about what that projectile will really do, but momentum will.

If the bullet stops in the target then force is calculated by dividing the momentum of the projectile by the time it takes the projectile to come to a stop in the target after initially hitting it. In other words, if momentum is telling you anything then force is telling you even more.

So it is pretty obvious that there is a lot of confusion over the name of both. Maybe we should all switch to metric.

There's really no confusion in general. I believe your confusion has arisen because you have thoroughly messed up the formulas & units that you're using. If you based any of your conclusions or analysis on the formulas or units you have listed in your posts then you need to start over from scratch.

If you like momentum then that's great. However, based on the level of knowledge of the topic you've displayed in this thread, it's clearly not worthwhile for you to try to justify this preference mathematically/scientifically nor is it reasonable for you to assert that understanding momentum is easier than understanding energy.

 

[Oro]

I think it would also be important, I think, at this point to put these energy figures in perspective. A smart fastball in an MLB game will carry right at 100 ft/lbs of energy if I recall correctly (at high-90s mph).

As we know, the catcher's body absorbs all that energy with barely a flinch (some is translated as heat in the glove). So we can extrapolate that a 300 or 400 ft/lb energy level is not enough to "knock down" an average man. Should it penetrate through and through, it's also going to take 1/2 or more of it's energy and go deposit that somewhere else entirely.

While the OP did not say that that absolute muzzle energy was his goal, this is a great place to point out that there are much, much more important factors to consider about a cartridge's effectiveness than it's muzzle energy. Penetration, expansion, and location. When you really dig into the physics, it's clear that kinetic energy (muzzle energy) is not that important as an absolute guide in choosing a cartridge in most of the popular/common handgun cartridges. In rifles, it becomes more interesting because the absolute differences become much more significant.

 

[JSmith]

E = 1/2 * m * v^2 tells me something, but it doesn't tell me everything. The velocity component outweighs mass by a great deal, but that's not the whole story. Much depends on what I'm shooting at. Do I want to shoot an intruder with a .17 cal 20-gr projectile at ~4000 fps, or a .45 cal 230-gr at 850 fps?

 

[harrygunner]

Collisions involve energy AND momentum. They are inseparable.

At every instance of a bullet's travel, conservation of BOTH momentum and energy are adhered to. Attempting to ignore one or the other leads to nonsense.

I don't expect to change gun forum discussions on this.

When it comes to understanding physics, at a minimum, it would be nice to see 'speed' used instead of 'velocity'. I've seen thousands of posts of bullet speeds but, no one has ever posted a velocity.

Sorry, carry on.

 

[JohnKSa]

When it comes to understanding physics, at a minimum, it would be nice to see 'speed' used instead of 'velocity'. I've seen thousands of posts of bullet speeds but, no one has ever posted a velocity.

Exactly how do the formulas for momentum and energy change when one uses "speed" instead of "velocity"?

 

[harrygunner]

Hi John.

I know you're kidding, but if you ever see a post from "me" saying something like "My 10mm ammo has a velocity of 1200 ft/s.", then you'll know someone has stolen my login password.

(If a unit vector is included in a well defined reference system, then it may have been me, but only if I've lost my mind.)